TY - JOUR
T1 - Superconvergent Cluster Recovery Method for the Crouzeix-Raviart Element
AU - Zhang , Yidan
AU - Chen , Yaoyao
AU - Huang , Yunqing
AU - Yi , Nianyu
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 508
EP - 526
PY - 2021
DA - 2021/01
SN - 14
DO - http://doi.org/10.4208/nmtma.OA-2020-0117
UR - https://global-sci.org/intro/article_detail/nmtma/18609.html
KW - Crouzeix-Raviart element, gradient recovery, superconvergent cluster recovery.
AB - <p style="text-align: justify;">In this paper, we propose and numerically investigate a superconvergent
cluster recovery (SCR) method for the Crouzeix-Raviart (CR) element. The proposed
recovery method reconstructs a $C^0$ linear gradient. A linear polynomial approximation is obtained by a least square fitting to the CR element approximation at certain
sample points, and then taken derivatives to obtain the recovered gradient. The SCR
recovery operator is superconvergent on uniform mesh of four patterns. Numerical
examples show that SCR can produce a superconvergent gradient approximation for
the CR element, and provide an asymptotically exact error estimator in the adaptive
CR finite element method.</p>